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#1 2005-09-12 10:58:32

mikau
Member
Registered: 2005-08-22
Posts: 1,504

stuck on logarthimic equation

2 log (x+2) + log (x - 1) = 3 log x            using a base of 3.

I'm supposed to solve for X. Usually I'm pretty good with these but this I just can't solve. Usually I have to factor, but I keep ending up with a 3rd degree polynomial which my mathbook has not taught me how to solve. So I'm expected to solve it another way. Help! :-(


A logarithm is just a misspelled algorithm.

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#2 2005-09-12 13:23:35

kylekatarn
Member
Registered: 2005-07-24
Posts: 445

Re: stuck on logarthimic equation

hi!
Its very simple indeed... I bet you stopped trying when you saw the x³....if you continue with the simplifications you end up with a easy quadratic.

Since we have all logs @ same base we don't need the info "using a base of 3"

And because I'm a bit lazy today (:|), let l(u) denote the logarithm of the expression u

2l(x+2) + l(x-1) = 3 l(x)
//I assume you know how to manipulate logs.
l[ (x+2)² ] + l(x-1) = l(x³)
l[ (x+2)².(x-1) ] = l(x³)

//if we have l(z)=l(w) we can solve [z=w] with [z and w >0]
(x+2)².(x-1) = x³; x>1

//now this is the fun part
(x+2)².(x-1) = x³
(x²+4x+4).(x-1) = x³
x³+4x²+4x-x²-4x-4 = x³
x³+4x²-x²-4 = x³
+x³+3x²-4 = +x³
3x²-4 = 0

//I told you it was easy!
3x²-4 = 0
3x² = 4
x² = 4/3
x = ±(2√3)/3

//remember the original equation's condition?? X>1
//we discard the negative solution, so the answer to the problem is

x=(2√3)/3



//omg...solving problems like these one makes me remember how I deeply miss my good ol' math classes.;|

Last edited by kylekatarn (2005-09-12 13:26:40)

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